beam2.f90 running
E= 1.00000000000000E+01 I= 9.00000000000000E+00 W= 7.00000000000000E+00
L= 8.00000000000000E+00 h:= 1.00000000000000E+00 n:= 9
Analytic Solution.
beam x:= 0.00000000000000E+00  y:=-0.00000000000000E+00
                       slope:= 0.00000000000000E+00
beam x:= 1.00000000000000E+00  y:=-1.98495370370370E-02
                       slope:=-3.40277777777778E-02
beam x:= 2.00000000000000E+00  y:=-5.83333333333333E-02
                       slope:=-3.88888888888889E-02
beam x:= 3.00000000000000E+00  y:=-9.11458333333333E-02
                       slope:=-2.43055555555556E-02
beam x:= 4.00000000000000E+00  y:=-1.03703703703704E-01
                       slope:=-3.94745964311167E-17
beam x:= 5.00000000000000E+00  y:=-9.11458333333333E-02
                       slope:= 2.43055555555556E-02
beam x:= 6.00000000000000E+00  y:=-5.83333333333333E-02
                       slope:= 3.88888888888889E-02
beam x:= 7.00000000000000E+00  y:=-1.98495370370370E-02
                       slope:= 3.40277777777778E-02
beam x:= 8.00000000000000E+00  y:=-0.00000000000000E+00
                       slope:=-7.89491928622334E-17
Numerical Solution.
Fourth order difference equation solution
boundary dy/dx:=0 fourth order
n= 7, h= 1.00000000000000E+00
solve A y := F for y 
                           A                            F 
 4.80000000000000E+01
-3.60000000000000E+01
 1.60000000000000E+01
-3.00000000000000E+00
 0.00000000000000E+00
 0.00000000000000E+00
 0.00000000000000E+00
 0.00000000000000E+00
-4.00000000000000E+00
 6.00000000000000E+00
-4.00000000000000E+00
 1.00000000000000E+00
 0.00000000000000E+00
 0.00000000000000E+00
 0.00000000000000E+00
-9.72222222222222E-03
 1.00000000000000E+00
-4.00000000000000E+00
 6.00000000000000E+00
-4.00000000000000E+00
 1.00000000000000E+00
 0.00000000000000E+00
 0.00000000000000E+00
-9.72222222222222E-03
 0.00000000000000E+00
 1.00000000000000E+00
-4.00000000000000E+00
 6.00000000000000E+00
-4.00000000000000E+00
 1.00000000000000E+00
 0.00000000000000E+00
-9.72222222222222E-03
 0.00000000000000E+00
 0.00000000000000E+00
 1.00000000000000E+00
-4.00000000000000E+00
 6.00000000000000E+00
-4.00000000000000E+00
 1.00000000000000E+00
-9.72222222222222E-03
 0.00000000000000E+00
 0.00000000000000E+00
 0.00000000000000E+00
 1.00000000000000E+00
-4.00000000000000E+00
 6.00000000000000E+00
-4.00000000000000E+00
-9.72222222222222E-03
 0.00000000000000E+00
 0.00000000000000E+00
 0.00000000000000E+00
-3.00000000000000E+00
 1.60000000000000E+01
-3.60000000000000E+01
 4.80000000000000E+01
 0.00000000000000E+00
fourth order difference equations are exact within
numerical accuracy when solution is fourth order.
x:=0.0  y:=0.0  boundary
x:= 1.00000000000000E+00 y:= -1.98495370370369E-02
x:= 2.00000000000000E+00 y:= -5.83333333333329E-02
x:= 3.00000000000000E+00 y:= -9.11458333333326E-02
x:= 4.00000000000000E+00 y:= -1.03703703703703E-01
x:= 5.00000000000000E+00 y:= -9.11458333333327E-02
x:= 6.00000000000000E+00 y:= -5.83333333333329E-02
x:= 7.00000000000000E+00 y:= -1.98495370370369E-02
x:= 8.00000000000000E+00  y:=0.0  boundary